I thought I’d share my recent experiences in case it’s of use / interest to anyone I the group:
I’d noticed a slight buzz coming from the D string so contacted my friendly local luthier who supplied this information:
1. As it is mainly when double stopping, then maybe the slot in the bridge on the D string has deepened to the point it causes buzzing, slacken the D and move the string out of the nick on top of the bridge, if the nick is narrow and deep (I.e deeper than 1/2 the thickness of the string), then try to widen it slightly then use a pencil to lubricate the slot.
2. How old and what type is the string?……old strings can get tired and wound ones can buzz when past their best
3. Check the chinrest and tailpiece for loose bits, screws, tailgut under the tailpiece touching the belly etc.
4. Make sure there is nothing IN the violin that may not rattle, but nevertheless is alien, I.e piece of cardboard, I’ve seen felt tip pen tops made sticky with toffee!
Try these options first, see how you get on.
It turned out I just needed new strings but I did use a pencil to lubricate the bridge slots as well.
Also: I have a vintage fiddle and found that Dominants strings wouldn’t fit in the fine tuners slots so I had to replace like for like with Pirastro Tonicas instead, which are fine but don’t seem to last very long!